02 آذر 1403
ابوالحسن رزمي نيا

ابوالحسن رزمی نیا

مرتبه علمی: دانشیار
نشانی: دانشکده مهندسی سیستم های هوشمند و علوم داده - گروه مهندسی برق
تحصیلات: دکترای تخصصی / مهندسی برق
تلفن: 07731222164
دانشکده: دانشکده مهندسی سیستم های هوشمند و علوم داده

مشخصات پژوهش

عنوان An Extended Formulation of Calculus of Variations for Incommensurate Fractional Derivatives with Fractional Performance Index
نوع پژوهش مقالات در نشریات
کلیدواژه‌ها
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مجله NONLINEAR DYNAMICS
شناسه DOI
پژوهشگران ابوالحسن رزمی نیا (نفر اول) ، وحید جوهری مجد (نفر دوم) ، احمد فیض دیزجی (نفر سوم)

چکیده

In this paper, we consider the main problem of variational calculus when the derivatives are Riemann–Liouville-type fractional with incommensurate orders in general. As the most general form of the performance index, we consider a fractional integral form for the functional that is to be extremized. In the light of fractional calculus and fractional integration by parts, we express a generalized problem of the calculus of variations, in which the classical problem is a special case. Considering five cases of the problem (fixed, free, and dependent final time and states), we derive a necessary condition which is an extended version of the classical Euler–Lagrange equation. As another important result, we derive the necessary conditions for an optimization problem with piecewise smooth extremals where the fractional derivatives are not necessarily continuous. The latter result is valid only for the integer order for performance index. Finally, we provide some examples to clarify the effectiveness of the proposed theorems.